{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Calculate Von Neumann Entropy and Purity for Dicke-Basis density matrix in presence of homogeneous local dissipation\n", "\n", "Author: Nathan Shammah, nathan.shammah@gmail.com\n", "\n", "We provide a tutorial for the task of calculating nonlinear functions of the denisty matrix, such as the Von Neumann entropy and purity, using the Dicke-Basis formalism in an open Lindblad dynamics characterized by (collective and) homogeneous local incoherent processes [1,2].\n", "\n", "For an introduction to the `qutip.piqs` module, see [The Introductory Notebook](https://nbviewer.jupyter.org/github/qutip/qutip-notebooks/blob/master/examples/piqs-overview.ipynb) or see Ref. [1].\n", "\n", "We provide an example of three bases that can be used the dynamics of a spin system on a lattice with all-to-all connectivity or of an ensemble of two-level systems in cavity QED. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from qutip import *\n", "from qutip.piqs import *\n", "from scipy.sparse import block_diag\n", "from scipy.sparse.linalg import eigsh, eigs\n", "from scipy import log" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define some auxiliary functions" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def plot_rho(rho, title=None):\n", " \"\"\"\n", " Plot the image show of the real values of a Qobj operator.\n", " \n", " Input:\n", " ------\n", " rho : :class: qutip.Qobj\n", " Density matrix or operator.\n", " Returns:\n", " ------\n", " figure : matplotlib.pyplot.figure\n", " Figure showing real part of matrix elements of the density matrix.\n", " \"\"\" \n", " plt.figure()\n", " plt.imshow(np.real(rho.full()))\n", " if title is not None:\n", " plt.title(title)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def spin_hamiltonian(N,h,basis=\"jmat\"):\n", " \"\"\"\n", " Calculate generalized spin Hamiltonian in the `jmat`, `dicke` or `uncoupled` basis.\n", " \n", " Input:\n", " ------\n", " N : int\n", " Number of spins.\n", " h : float\n", " Magnitude of transverse (Jx) external magnetic field, of size (N+1).\n", " basis : string, (default='jmat')\n", " Basis of the Hamiltonian. \n", " Can be 'jmat' (N+1), 'dicke' (O(N^2)), or \"uncoupled\" (2^N). \n", " Returns:\n", " ------\n", " hamiltonian_spin : qutip.Qobj()\n", " Hamiltonian of the system in the given basis (default is `jmat`).\n", " \"\"\"\n", " if basis==\"jmat\":\n", " jx,jy,jz = jmat(N/2)\n", " elif basis==\"dicke\":\n", " jx,jy,jz = jspin(N, basis=\"dicke\")\n", " elif basis==\"uncoupled\":\n", " jx,jy,jz = jspin(N, basis=\"uncoupled\")\n", " \n", " hamiltonian_spin = (jz**2)-h*jx\n", " return hamiltonian_spin" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualizing the density matrix structure" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 4\n", "# Compact Dicke basis (O(N^3))\n", "rho_dicke = Qobj(block_matrix(N,elements=\"degeneracy\"))\n", "plot_rho(rho_dicke, title='Dicke basis, $N={}$'.format(N))\n", "# Expanded Dicke basis (2^N)\n", "expanded_dicke_blocks = dicke_blocks_full(Qobj(block_matrix(N,elements=\"ones\")))\n", "rho_dicke_extended = Qobj(block_diag(expanded_dicke_blocks))\n", "plot_rho(rho_dicke_extended, title='Expanded Dicke basis, $N={}$'.format(N))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the color plots above, we show the crucial difference between the representative of the density matrix in the Dicke basis used by `qutip.piqs` (top panel) and the expanded object, which is the actual density matrix with all the degenerate blocks. All the information on the density matrix is contained already in the compact representative density matrix, which can be used to derive the dynamics, but in order to correctly calculate nonlinear properties of the density matrix, in presence of homogenous local processes, one needs to properly account for the non-symmetrical degenerate blocks, as shown below. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the all-to-all spin Hamiltonian" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# define the spin Hamiltonian\n", "h = 0.1\n", "H = spin_hamiltonian(N,h)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "h_jmat = spin_hamiltonian(N,h,basis=\"jmat\")\n", "h_uncoupled = spin_hamiltonian(N,h,basis=\"uncoupled\")\n", "h_dicke = spin_hamiltonian(N,h,basis=\"dicke\")\n", "eigvals_dicke, eigvecs_dicke = h_dicke.eigenstates()\n", "eigvals_uncoupled, eigvecs_uncoupled = h_uncoupled.eigenstates()\n", "eigvals_jmat, eigvecs_jmat = h_jmat.eigenstates()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# spin operators\n", "jx_jmat,jy_jmat,jz_jmat = jmat(N/2)\n", "jm_jmat = jmat(N/2,\"-\")\n", "jx_dicke,jy_dicke,jz_dicke = jspin(N, basis=\"dicke\")\n", "jm_dicke = jspin(N, \"-\",basis=\"dicke\")\n", "jx_uncoupled,jy_uncoupled,jz_uncoupled = jspin(N, basis=\"uncoupled\")\n", "jm_uncoupled = jspin(N, \"-\",basis=\"uncoupled\")" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "excited_dicke = excited(N,basis=\"dicke\")\n", "excited_uncoupled = excited(N,basis=\"uncoupled\")\n", "rho0_dicke = excited_dicke\n", "rho0_uncoupled = excited_uncoupled" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# create local operators (0.5*Pauli matrices)\n", "sx_list, sy_list, sz_list = spin_algebra(N)\n", "sm_list = []\n", "sp_list = []\n", "for i in range(0,len(sx_list)):\n", " sm_list.append(sx_list[i] - 1j*sy_list[i])\n", " sp_list.append(sx_list[i] + 1j*sy_list[i])\n", "jp_uncoupled = jm_uncoupled.dag()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Defining the dissipation rates and building the Liouvillian superoperator" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "N = 4\n", "Hilbert space dim = (9, 9)\n", "Number of Dicke states = 9\n", "Liouvillian space dim = (81, 81)\n", "emission = 0.05\n", "dephasing = 0.15707963267948966\n", "pumping = 0.015\n" ] } ], "source": [ "# rates of local and collective incoherent processes \n", "gamma_local_down = 0.05 \n", "gamma_local_up = 0.3*gamma_local_down\n", "gamma_local_phi = np.pi*gamma_local_down\n", "# create local collapse operators\n", "# full space (2^N Hilbert space, uncoupled basis)\n", "c_ops_local = []\n", "for i in range(0,len(sx_list)):\n", " c_ops_local.append(np.sqrt(gamma_local_down)*sm_list[i])\n", " c_ops_local.append(np.sqrt(gamma_local_up)*sm_list[i].dag())\n", " c_ops_local.append(np.sqrt(gamma_local_phi)*sz_list[i])\n", "# Dicke space (N^2 Hilbert space for the density matrix, coupled basis)\n", "ensemble = Dicke(N)\n", "ensemble.hamiltonian = h_dicke\n", "ensemble.emission = gamma_local_down\n", "ensemble.pumping = gamma_local_up\n", "ensemble.dephasing = gamma_local_phi\n", "#ensemble.collective_emission = gamma_local_down\n", "print(ensemble)\n", "liouvillian_local_dicke = ensemble.liouvillian()\n", "liouvillian_local_uncoupled = liouvillian(0*h_uncoupled,c_ops=c_ops_local)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving the time evolution of the Lindblad master equation" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dicke local ok\n", "uncoupled local ok\n" ] } ], "source": [ "# time \n", "times = np.linspace(0,50,500)\n", "## local dissipation only \n", "storing = Options(store_states=True)\n", "store = True\n", "# Dicke\n", "result_local_dicke = mesolve(liouvillian_local_dicke,rho0_dicke,times, \n", " c_ops=[], \n", " e_ops=[jx_dicke,jy_dicke,jz_dicke,\n", " jx_dicke**2,jy_dicke**2, \n", " jz_dicke**2,jm_dicke.dag()],\n", " options=storing)\n", "jxt_local_dicke = result_local_dicke.expect[0]\n", "jyt_local_dicke = result_local_dicke.expect[1]\n", "jzt_local_dicke = result_local_dicke.expect[2]\n", "jxxt_local_dicke = result_local_dicke.expect[3]\n", "jyyt_local_dicke = result_local_dicke.expect[4]\n", "jzzt_local_dicke = result_local_dicke.expect[5]\n", "jpt_local_dicke = result_local_dicke.expect[6]\n", "if store == True:\n", " rhot_local_dicke = result_local_dicke.states\n", "print(\"Dicke local ok\")\n", "# full\n", "result_local_uncoupled = mesolve(h_uncoupled,rho0_uncoupled,times, \n", " c_ops=c_ops_local,\n", " e_ops=[jx_uncoupled,jy_uncoupled,jz_uncoupled,\n", " jx_uncoupled**2,jy_uncoupled**2, \n", " jz_uncoupled**2,\n", " jp_uncoupled],\n", " options=storing)\n", "jxt_local_uncoupled = result_local_uncoupled.expect[0]\n", "jyt_local_uncoupled = result_local_uncoupled.expect[1]\n", "jzt_local_uncoupled = result_local_uncoupled.expect[2]\n", "jxxt_local_uncoupled = result_local_uncoupled.expect[3]\n", "jyyt_local_uncoupled = result_local_uncoupled.expect[4]\n", "jzzt_local_uncoupled = result_local_uncoupled.expect[5]\n", "jpt_local_uncoupled = result_local_uncoupled.expect[6]\n", "if store == True:\n", " rhot_local_uncoupled = result_local_uncoupled.states\n", "print(\"uncoupled local ok\")\n", "\n", "j2t_local_dicke = jxxt_local_dicke+jyyt_local_dicke+jzzt_local_dicke\n", "j2t_local_uncoupled = jxxt_local_uncoupled+jyyt_local_uncoupled+jzzt_local_uncoupled" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plotting the evaluated results (*linear* functions of the density matrix)\n", "Here we plot the values of some observables in time, using the relation\n", "\\begin{eqnarray}\n", "\\langle A(t)\\rangle&=& \\text{Tr}[\\rho(t)A],\n", "\\end{eqnarray}\n", "which is linear with respect to $\\rho$. For this reason, handling the compact Dicke-basis representative of the density matrix, given by `qutip.piqs`, gives same results to handling the expanded-blocks density matrix. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fs = 15 # font size\n", "plt.figure(figsize=(16,6))\n", "plt.subplot(121)\n", "plt.title(\"Dicke vs uncoupled basis: local dynamics, N={}\".format(N))\n", "plt.plot(jxxt_local_dicke/N**2,\"r-\", label = \"$\\\\langle J_x^2 \\\\rangle $ dicke, $N^3$\")\n", "plt.plot(jxxt_local_uncoupled/N**2,\".\", label = \"$\\\\langle J_x^2 \\\\rangle $ uncoupled, $2^N$\")\n", "plt.legend(fontsize=fs*0.8)\n", "plt.subplot(122)\n", "plt.title(\"uncoupled: local dynamics\")\n", "plt.plot(j2t_local_dicke/N**2,\"s\", label = \"$\\\\langle J^2 \\\\rangle/N^2 $ Dicke, $2^N$\")\n", "plt.plot(j2t_local_uncoupled/N**2,\"k--\", label = \"$\\\\langle J^2 \\\\rangle/N^2 $ uncoupled, $2^N$\")\n", "plt.legend(fontsize=fs*0.8)\n", "plt.suptitle(\"Jx and Jz in time: Collective vs local dynamics, N={}\".format(N))\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the time plots above, we show how the solutions obtained from `mesolve` in the two formalisms match with each other. The Dicke basis calculations require only $N^3$ resources, whereas the uncoupled basis requires $ 2^N$ Hilbert spaces. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Efficiently calculating the Von Neumann Entropy in the Dicke basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Von Neumman entropy is a generalization of the Shannon entropy to quantum systems. It is also used in some cases as a witness of entanglement, for bipartite closed systems. Here we show that this nonlinear function of the density matrix can be calculated over the *representative* of the Dicke-basis density matrix, used above, by taking into account the correct weight of non-symmetrical subspaces of the total Hilbert space. \n", "\n", "A general function is defined to perform this weighted sum, `dicke_function_trace`, which is used by `entropy_vn_dicke`, keeping the resources only polynomial with respect to the number of qubits or two-level systems. \n", "\n", "A check with respect to this function is performed below by using, for small $N$, the results from the uncoupled basis ($2^N$) and also by expanding, in a non-efficient way, the Dicke-basis density matrix into an object that is placed in the $2^N$ Hilbert space, by accounting explicitly for the degeneracy of each block of the density matrix in the Dicke formalism, using the function `dicke_blocks_full`. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "entropy_wrong = []\n", "entropy_uncoupled = []\n", "entropy_dicke = []\n", "entropy_dicke_overhead = []\n", "# uncoupled basis (2^N)\n", "for i in range(len(rhot_local_uncoupled)):\n", " entropy_uncoupled.append(entropy_vn(rhot_local_uncoupled[i]))\n", "# use density matrix calculated in the Dicke basis \n", "for i in range(len(rhot_local_dicke)):\n", " entropy_wrong.append(entropy_vn(rhot_local_dicke[i]) )\n", " entropy_dicke_overhead.append(entropy_vn(Qobj(block_diag(dicke_blocks_full(rhot_local_dicke[i])))))\n", " entropy_dicke.append(entropy_vn_dicke(rhot_local_dicke[i]))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "plt.plot(times,entropy_wrong,\"-\",label=\"dicke (unweighted blocks, wrong)\")\n", "plt.plot(times,entropy_dicke_overhead,\"--\",label=\"dicke (2^N overhead))\")\n", "plt.plot(times,entropy_dicke,\"--\",linewidth = 4,label=\"dicke (efficient)\")\n", "plt.plot(times,entropy_uncoupled,linewidth = 2,label=\"uncoupled basis (2^N)\")\n", "plt.xlabel(\"time\")\n", "plt.ylabel(\"Von Neumann entropy of $\\\\rho(t)$\")\n", "plt.title(\"Dynamics with homogeneous local dissipation\")\n", "plt.legend()\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As expected, there are three equivalent methods that can be used to calculate the Von Neumann entropy. \n", "By calculating it in a straightforward way from the *representative* of the density matrix in the Dicke basis formalism, the result is wrong, as it under-weighs the contribution from non-fully symmetric subspaces, corresponding to all the blocks on the right of the first block in the density matrix representation. \n", "\n", "Above, we use an efficient method to account for the Von Neumann entropy of the density matrix, using the `entropy_vn_dicke` function. This function applies the Von Neumann entropy function to each block of the density matrix, accounted with the correct degeneracy using the `dicke_function_trace` present in `qutip.piqs`. Similarly, in the next blocks the `purity_dicke` function will be calculated. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Purity of density matrices in the Dicke basis" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "purity_uncoupled = []\n", "purity_dicke_list = []\n", "purity_dicke_full = []\n", "purity_wrong = []\n", "for i in range(len(rhot_local_uncoupled)):\n", " # inefficient method\n", " purity_uncoupled.append((rhot_local_uncoupled[i]**2).tr())\n", "for i in range(len(rhot_local_dicke)):\n", " # efficient method\n", " purity_dicke_list.append(purity_dicke(rhot_local_dicke[i]) )\n", " # inefficient method (scales with 2^N)\n", " rho_dicke_expanded = Qobj(block_diag(dicke_blocks_full(rhot_local_dicke[i])))\n", " purity_dicke_full.append((rho_dicke_expanded**2).tr())\n", " # wrong approach\n", " purity_wrong.append((rhot_local_dicke[i]**2).tr()) " ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot()\n", "plt.plot(times,purity_uncoupled,label=\"uncoupled\", linewidth=4)\n", "plt.plot(times,purity_dicke_list,\"--\",label=\"dicke (efficient)\", linewidth=6)\n", "plt.plot(times,purity_dicke_full,\"--\",label=\"dicke (inefficient)\")\n", "plt.plot(times,purity_wrong,\"-\",label=\"dicke (unweighted blocks, wrong)\")\n", "plt.xlabel(\"time\")\n", "plt.ylabel(\"Purity of $\\\\rho(t)$\")\n", "plt.legend()\n", "plt.title(\"Dynamics with homogeneous local dissipation\")\n", "plt.show()\n", "plt.close()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the plot above we see that the three equivalent methods give the correct result. The user can define its own nonlinear functions, beyond entropy and purity, of the density matrix by using `dicke_function_trace`. " ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "QuTiP: Quantum Toolbox in Python\n", "================================\n", "Copyright (c) QuTiP team 2011 and later.\n", "Original developers: R. J. Johansson & P. D. Nation.\n", "Current admin team: Alexander Pitchford, Paul D. Nation, Nathan Shammah, Shahnawaz Ahmed, Neill Lambert, and Eric Giguère.\n", "Project Manager: Franco Nori.\n", "Currently developed through wide collaboration. See https://github.com/qutip for details.\n", "\n", "QuTiP Version: 4.4.0\n", "Numpy Version: 1.17.1\n", "Scipy Version: 1.2.1\n", "Cython Version: 0.29.8\n", "Matplotlib Version: 3.0.3\n", "Python Version: 3.7.3\n", "Number of CPUs: 2\n", "BLAS Info: OPENBLAS\n", "OPENMP Installed: False\n", "INTEL MKL Ext: False\n", "Platform Info: Darwin (x86_64)\n", "Installation path: /miniconda3/lib/python3.7/site-packages/qutip\n", "==============================================================================\n", "Please cite QuTiP in your publication.\n", "==============================================================================\n", "For your convenience a bibtex reference can be easily generated using `qutip.cite()`\n" ] } ], "source": [ "qutip.about()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References \n", "[1] N. Shammah, S. Ahmed, N. Lambert, S. De Liberato, and F. Nori, *Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance\", Phys. Rev. A **98**, 063815 (2018), https://arxiv.org/abs/1805.05129, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063815.\n", "\n", "[2] L. Novo, T. Moroder, and O. Gühne, *Genuine multiparticle entanglement of permutationally invariant states*, Phys. Rev. A **88**, 012305 (2013). https://journals.aps.org/pra/abstract/10.1103/PhysRevA.88.012305" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }